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Sep 20, 2013
09/13

by
Helmer Aslaksen; Mong Lung Lang

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Let $R$ be an indecomposable root system. It is well known that any root is part of a basis $B$ of $R$. But when can you extend a set of two or more roots to a basis $B$ of $R$? A $\pi$-system is a linearly independent set of roots, $C$, such that if $\alpha$ and $\beta$ are in $C$, then $\alpha - \beta$ is not a root. We will use results of Dynkin and Bourbaki to show that with two exceptions, $A_3 \subset B_n$ and $A_7 \subset E_8$, an indecomposable $\pi$-system whose Dynkin diagram is a...

Source: http://arxiv.org/abs/math/0410357v3

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32

Sep 20, 2013
09/13

by
Helmer Aslaksen; Vesselin Drensky; Liliya Sadikova

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Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultameous conjugation by $GL_n$ is generated by traces of products of generic matrices. Teranishi, 1986, found a minimal system of eleven generators of the algebra of invariants of two $3\times 3$ matrices. Nakamoto, 2002, obtained an explicit, but very complicated, defining relation for a similar system of generators over $\mathbb Z$. In this paper we have found another natural set of eleven...

Source: http://arxiv.org/abs/math/0405389v2

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Oct 27, 2014
10/14

by
Hovlid, Einar; Bukve, Oddbj?rn; Haug, Kjell; Aslaksen, Aslak Bjarne; von Plessen, Christian

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This article is from BMC Health Services Research , volume 12 . Abstract Background: Changes that improve the quality of health care should be sustained. Falling back to old, unsatisfactory ways of working is a waste of resources and can in the worst case increase resistance to later initiatives to improve care. Quality improvement relies on changing the clinical system yet factors that influence the sustainability of quality improvements are poorly understood. Theoretical frameworks can guide...

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3532388